To simplify the expression \( 36x - 216x^2 - 36 \), we can factor it.
First, we can notice that each term can be divided by 36:
\[ 36x - 216x^2 - 36 = 36(x - 6x^2 - 1) \]
Next, we can reorder the terms inside the parentheses:
\[ 36(-216x^2 + 36x - 36) = 36(-6(x^2 - 6x + 1)) \]
Now, we can factor the quadratic expression further if possible. However, this simplifies down incorrectly if we try further complexity, so we keep it straightforward. Simplifying can yield:
We can factor out the \( -6 \):
\[ -6(6x^2 - 6x + 6) \]
However, this ultimately does not lead to any basic reduction on \( x \). Let’s return to the standard factorization where we see if we can take 36 out of \( x \) elements directly.
The correct simplification looks at common factors directly:
Factoring out \( -6 \) yields:
\[ = -6(6x^2 - 36x + 6) \]
Final expression can give insight, but it’s still handled lightly, \( = 6(6x - 36)/x = \).
Thus, we can affirm that:
The expression is ultimately simplified to:
\[ 27 + 6 \]
In simplest form, terms lead us to the factor directly on division evaluates into \( 6 \) as leading factors remain. Thus the easiest path reveals through:
The answer is thus \( 6x \).
3 answers